《凝聚态拓扑物理》教学大纲

一、课程基本信息

开课单位: 物质科学与技术学院 课程代码: PHYS2122
课程名称: 凝聚态拓扑物理 英文名称: Topology in Condensed Matters
学 分: 2 学 时: 32
授课对象:   授课语言: 中英文
先修课程:

二、课程简介和教学目的

对称破缺是物理学的一个重要概念。在研究多数凝聚态物理体系的时候,我们最在意的问题是:这个系统的对称性是什么?一旦掌握了体系的所有对称操作,对应的本征状态以及物理图像都变得清晰。然而在某些情况下,这种理念并不能揭示出一个体系最本质的内禀属性。事实上更重要的问题是:这个系统哪些特性与对称性无关?拓扑正是研究一个对象与具体的几何形状无关的那些性质的学科。也是这门课程着重讨论的话题。

拓扑学作为数学的一个分支已经建立了成熟的框架。把拓扑的核心概念引入到理解凝聚态体系中,成功的解释和预测了很多新奇的物理现象,并发现了一系列极富前景的量子材料。这也是近10年来活跃在凝聚态物理前沿的课题。用拓扑的方式去处理物理问题是当代凝聚态物理重要的标志(2016诺贝尔物理奖)。因此,将这种新的理念作为教学课程让学生的物理素养与时俱进,对培养物质学院科研人才有着重要意义。《凝聚态拓扑物理》这门课致力成为上科大的特色课程。本课程与我校国际领先科研资源相呼应:上科大拓扑物理实验室平台的建立为学生提供了良好的教学平台,能够让学生亲身体验拓扑物理最前沿科研的观点的方法论。

本课程的教授对象为物质学院对探索凝聚态实验以及量子材料有浓厚的兴趣的本科生/研究生。在课程中我将尽量避免冗繁的数学,重点放在用拓扑的方法重新理解一系列凝聚态系统中的物理原理:如何应用拓扑,如何寻找拓扑性质,以及如何进行观测。课程包括4个部分,8个章节,32学时。

三、教学内容、教学方式和学时安排

课堂教学内容

教学进度和学时安排

教学方式

第1章 拓扑物理导论

第1周

2学时

课堂教学、课后复习(作业)、文献阅读

第2章 二次量子化

第2-5周

8学时

课堂教学、课后复习(作业)、文献阅读

第3章 量子体系的几何相位

第6-7周

4学时

课堂教学、课后复习(作业)、文献阅读

第4章 二能级系统:SSH模型

第8周

2学时

课堂教学、课后复习(作业)、文献阅读

第5章 磁单极子的量子化

第9周

2学时

课堂教学、课后复习(作业)、文献阅读

第6章 量子霍尔体系和拓扑绝缘体

第10-12周

6学时

课堂教学、课后复习(作业)、文献阅读

第7章 实空间的拓扑

第13-14周

4学时

课堂教学、课后复习(作业)、文献阅读

第8章 总结和展望

第15周

2学时

课堂教学、课后复习(作业)、文献阅读

期末考试

第16周

闭卷考试




四、考核方式和成绩评定

最终成绩由平时作业成绩和期末考试两部分组成,其中作业成绩占40%,期末考试占60%。

五、推荐教材

书名 作者 译者 出版社 出版时间 ISBN

六、参考书目

书名 作者 译者 出版社 出版时间 ISBN

七、其他说明

八、教师信息和开课单位审核意见

授课教师

(签名)

    年   月   日
邮  箱 shilei.zhang@shanghaitech.edu.cn
电  话
开课单位审核意见

(签名)

                   年   月   日

《Topology in Condensed Matters》Syllabus

1.Basic course information

unit: School of Physical Science and Technology course code: PHYS2122
course name: 凝聚态拓扑物理 course name: Topology in Condensed Matters
credits: 2 period: 32
teaching object:   teaching language: Chinese and English
previous course:

2.Course introduction and teaching purpose

Symmetry breaking is one of the core concepts of condensed matter physics. To understand a system, the most important question to ask is: what is its underlying symmetry? Symmetry captures the fundamental physics needed to describe a system. Nevertheless, this philosophy does not always lead to complete understanding of a process. In some occasions, an even meaningful question to ask is: what are the properties that are independent of symmetry? The physics that are not affected by the geometrical properties are the key topics that will be discussed in this course (termed here as topology). Unlike symmetry arguments that deal with degeneration problems, those seemingly rare occasions that immune to geometrical changes will lead to fascinating consequences in condensed matters, from which one finds intrinsic implications of a quantum system.

The concept of topology has revolutionised condensed matter physics over the past decade, and keep spreading into a variety of research areas. Having a specialised course that introduces this magnificent philosophy becomes demanding for the purpose of training outstanding physicists. Moreover, the establishment of Topological Physics Laboratory in ShanghaiTech provides excellent opportunities for our students to percept this physics branch. <<Topology in Condensed Matters>> forms one of the unique lecture courses in ShanghaiTech, which aligns with the scope that our physics education embraces cutting-edge scientific researches.

This course is designed for undergraduate/graduate experimentalists who prepare to explore in-depth physics in condensed mater systems. I will focus on understanding a number of real systems from a topological perspective: how topological properties lead to novel physics, how to find those rare occasions, and how to measure them. I wish the students appreciate the elegancy of this mathematical concept, and will be able to apply it into their own studies.

3.Teaching content, teaching method and teaching time arrangement

Teaching Content

Teaching Time schedule

Teaching methods

Chapter 1: From Art, History to Mathematics: Some Perceptions

Week 1-2

3 classes

Class teaching, homework, literature reading

Chapter 2: Order Parameter and Broken Symmetry

Weeks 3-4

6 classes

Class teaching, homework, literature reading

Chapter 3: Geometric Phase in Quantum Systems

Weeks 5-6

6 classes

Class teaching, homework, literature reading

Chapter 4: Quantum Hall – The Meaning of Whole Numbers

Weeks 7-8

6 classes

Class teaching, homework, literature reading

Chapter 5: More Topologies in Momentum Space

Weeks 9-10

6 classes

Class teaching, homework, literature reading

Chapter 6: Kinks, Domain Walls, and Topological Defects

Weeks 11-12

6 classes

Class teaching, homework, literature reading

Chapter 7: Topologies in Ordered Media

Weeks 13-14

6 classes

Class teaching, homework, literature reading

Chapter 8: Topological Quantum Field and Its Computational Art 

Weeks 15-16

6 classes

Class teaching, homework, literature reading

Final Exam

Weeks 17-18


Close




4.Assessment methods and performance evaluation

Final score = 40% homework score + 60% final exam score

5.Other instructions

6.Teachers' information and audit institute

teacher

(signature)

    /   /   /
email shilei.zhang@shanghaitech.edu.cn
telephone
Institute of audit opinion

(signature)

                   /   /   /